The offices of McKinsey and Co, No 1 Jermyn Street, London
Photograph: Dan Chung for the Guardian

Behind the closed doors of five-star hotels and Michelin-starred restaurants, campaigning has begun in one of the world’s most secretive elections.

Candidates are not allowed to officially campaign, are prevented from submitting a manifesto and nearly all of the voters earn at least $1m a year. Welcome to the race to become the next managing partner of McKinsey & Company, the world’s largest management consultancy firm which provides very expensive advice to multinational companies and governments across the world.

While McKinsey advises its clients that transparency is “the most important driver” of improved performance, the consultancy firm refused to answer any questions about the process by which its partners are electing their new leader. The election, which informally began at the five-star Grosvenor House Hotel on Park Lane last month and will not conclude until the spring, is so secretive and archaic that its described it as similar to the conclave to elect a new Pope – bar the white smoke.

Whoever wins will become one of the best-connected people in the world. Dominic Barton, the current managing partner, meets two chief executive or government leaders every day and is on a plane 240 days a year. His hectic schedule, he says, gives him “a unique perspective on what matters to companies, governments, and non-profits the world over”.

The new boss will also have to manage a lot of giant egos within the firm, which is owned by its partners and has been compared to the US marines, the Jesuits, the Roman army and a corporate Mandarin elite.

“Our firm is full of leaders,” Barton, who known as Dom to his colleagues, said. “As managing director I set themes, make connections, and drive forward initiatives that will advance our ability to serve our clients, strengthen our firm, and develop our people.”

Duff McDonald, who describes the company as the “single greatest legitimiser of mass lay-offs … in modern history” in The Firm, his investigative book on McKinsey, said partners openly refer to themselves as “the greatest collection of talent the world has ever seen”.

He reports one partner stating that: “There are only three great institutions left in the world: the marines, the Catholic Church and McKinsey.”

The vote comes as McKinsey, which employs 29,000 people in 65 countries, is embroiled in the “state capture” controversy in South Africa. McKinsey is being investigated over allegations of bribery and corruption in relation to work it carried out for friends of the president, Jacob Zuma. It is the biggest crisis to hit the firm since former managing partner Rajat Gupta was jailed for insider dealing.

McKinsey denies the bribery allegations, but has admitted “violations of our professional standards” and apologised to the people of South Africa. Tom Barkin, its global chief risk officer, said the firm was “embarrassed” that work with a company linked to South Africa’s controversial billionaire Gupta family (no relation to Rajat Gupta) “fell short of our standards”.

Despite the denial and apology, McKinsey was this week dropped by two of its biggest South African clients – Barclays Africa and Standard Bank – as public pressure mounts on all those involved in the scandal, which has already led to the collapse of public relations firm Bell Pottinger.

At a series of recent meetings and dinners arranged for partners to begin the selection to find a replacement for Barton, the South African scandal and its impact on the firm’s fiercely guarded reputation was the main topic of conversation.

None of the early rumoured frontrunners to replace Barton, who will have led McKinsey for the maximum permitted three three-year terms, are from the South African office or linked to the scandal. The runners and riders are said to include: Vivian Hunt, managing partner of the UK and Ireland; Gary Pinkus, managing partner for north America; Kevin Sneader, chairman of the Asia-Pacific; and Bob Sternfels, head of global functions.

The nomination process will formally begin in January when partners each select seven candidates in their preferred order. All of McKinsey’s senior partners can be selected bar those over age 57 or planning to retire. The results of the first round will narrow the field to 10. A second round of voting in February will whittle the field down to a face-off, with the winner announced in March and taking up the position in July 2018. It’s not known how much money the managing partner or any other partner gets paid as McKinsey does not publish any financial figures, but Gupta was reportedly paid $6m a year.

“It really is the most unusual and secretive appointment process in the business,” said Matthew Gwyther, the recently departed editor of Management Today. “They keep the whole process very secret, it’s almost a papal conclave without the smoke coming up at the end. McKinsey is more secretive than that.

“They’re secretive in everything they do, which from a journalistic point of view makes them maddening as they very rarely talk about anything. The most you get is the McKinsey Quarterly magazine.” The magazine is not exactly a page-turner: the lead story in the most recent edition is about how “a combination of survey data, sophisticated statistical analysis, and modelling” explains the importance of digitisation.

Vivian Hunt, managing partner of the UK and Ireland. Photograph: McKinsey & Company

In his column in the latest issue, Barton says companies need a “new playbook” on gender equality as companies fail to recruit enough women to high-level jobs. “The old [playbook] isn’t working,” he says. “We need bolder leadership and more exacting execution.”

His comments on gender equality, which include the admission that McKinsey itself is finding it hard to make “deep and lasting progress”, has focused attention on Hunt. She is the firm’s lead speaker on how increasing diversity can improve companies’ performance. Hunt, who is an African American with dual British and American citizenship, is serially published on the topic including reports titled Women Matter, Diversity Matters, and The power of Parity: How advancing women’s equality can add $12tn to global growth.

Hunt, who has been named one of the 10 most influential black people in Britain by the Powerlist Foundation, serves on the board of the CBI London council and the mayor of London’s business advisory board and advises the Tate Modern, the Southbank Centre and Teach First.

Gwyther said the fight for the top job is expected to be brutal as McKinsey’s partners “really are the crème de la crème of the business world, and my God do they believe in themselves”. He said they’re right to an extent. “They really do get the best students from the best universities and the best of the crop of the business schools.”

The firm receives nearly 100 applications for each place on its yearly intake. But securing a place does not mean a McKinsey career for life: the firm operates a brutal “up or out” policy with a turnover rate of about 25%. It is suggested that if recruits do not make partner within five or six years, they might want to try their luck elsewhere. Barton though is an exception, having failed to make the grade at his first two attempts at partner.

Once firmly in place, partners stay McKinsey-ites even after leaving the firm. Former partners – who populate boardrooms and parliaments across the world – are known to still refer to themselves and their former colleagues as “we”. The firm is often the first port of call for expensive advice when ex-McKinsey people get a new top job, including Mark Carney, who asked the firm to review the Bank’s operations shortly after he was appointed governor.